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作者：Hassell, Andrew; Hillairet, Luc
摘要：Partially rectangular domains are compact two-dimensional Riemannian manifolds X, either closed or with boundary, that contain a flat rectangle or cylinder. In this paper we are interested in partially rectangular domains with ergodic billiard flow; examples are the Bunimovich stadium, the Sinai billiard or Donnelly surfaces. We consider a one-parameter family X-t of such domains parametrized by the aspect ratio t of their rectangular part. There is convincing theoretical and numerical evidenc...
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作者：Guralnick, Robert M.; Zieve, Michael E.
摘要：Let k be a field of characteristic p > 0, let q be a power of p, and let u be transcendental over k. We determine all polynomials f is an element of k[X]\k[X-p] of degree q(q-1)/2 for which the Galois group of f(X)-u over k(u) has a transitive normal subgroup isomorphic to PSL2(q), subject to a certain ramification hypothesis. As a consequence, we describe all polynomials f is an element of k[X] such that deg(f) is not a power of p and f is functionally indecomposable over k but f decomposes o...
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作者：Guralnick, Robert M.; Rosenberg, Joel; Zieve, Michael E.
摘要：We produce a new family of polynomials f(X) over fields k of characteristic 2 which are exceptional, in the sense that f(X) - f(Y) has no absolutely irreducible factors in k[X, Y] except for scalar multiples of X - Y; when k is finite, this condition is equivalent to saying that the map alpha bar right arrow f(alpha) induces a bijection on an infinite algebraic extension of k. Our polynomials have degree 2(e-1)(2(e) - 1), where e > 1 is odd. We also prove that this completes the classification...
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作者：Holowinsky, Roman
摘要：We approach the holomorphic analogue to the Quantum Unique Ergodicity conjecture through an application of the Large Sieve. We deal with shifted convolution sums as in [Ho109], with various simplifications in our analysis due to the knowledge of the Ramanujan-Petersson conjecture in this holomorphic case.
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作者：Ludwig, Monika; Reitzner, Matthias
摘要：A classification of upper semicontinuous and SL(n) invariant valuations on the space of n-dimensional convex bodies is established. As a consequence, complete characterizations of centro-affine and L-p affine surface areas are obtained. The proofs make use of a new SL(n) shaping process for convex bodies.
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作者：Beliaev, Dmitri; Smirnov, Stanislav
摘要：In many problems of classical analysis extremal configurations appear to exhibit complicated fractal structures, making it hard to describe them and to attack such problems. This is particularly true for questions related to the multifractal analysis of harmonic measure. We argue that, searching for extremals in such problems, one should work with random fractals rather than deterministic ones. We introduce a new class of fractals: random conformal snowflakes, and investigate their properties,...
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作者：Cass, Thomas; Friz, Peter
摘要：We consider stochastic differential equations dY = V (Y) dX driven by a multidimensional Gaussian process X in the rough path sense [ T. Lyons, Rev. Mat. Iberoamericana 14, (1998), 215-310]. Using Malliavin Calculus we show that Y-t admits a density for t is an element of (0, T] provided (i) the vector fields V = (V-1,...,V-d) satisfy Hormander's condition and (ii) the Gaussian driving signal X satisfies certain conditions. Examples of driving signals include fractional Brownian motion with Hu...
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作者：Brenner, Holger; Monsky, Paul
摘要：We give an example showing that tight closure does not commute with localization.
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作者：Nave, Lee S.
摘要：Using a generalized homotopy fixed point spectral sequence due to Hopkins and Miller, we show that the Smith-Toda complex V((p + 1)/2) does not exist for p a prime greater than 5. This extends earlier results of Toda and Ravenel for the primes 2, 3, and 5. It is also shown that if V((p - 1)/2) exists, it is not a ring spectrum.
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作者：Bruinier, Jan; Ono, Ken
摘要：Recent works, mostly related to Ramanujan's mock theta functions, make use of the fact that harmonic weak Maass forms can be combinatorial generating functions. Generalizing works of Waldspurger, Kohnen and Zagier, we prove that such forms also serve as generating functions for central values and derivatives of quadratic twists of weight 2 modular L-functions. To obtain these results, we construct differentials of the third kind with twisted Heegner divisor by suitably generalizing the Borcher...
